We show how to compute the local polar multiplicities of a germ at zero of an analytic variety Y in C p , which is the image by a finite morphism f : Z → Y , of a d-dimensional isolated complete intersection singularity Z in C n . We also show how to compute the local Euler obstruction of Y at zero in the case that it is reduced. For this we apply the formula due to Lê and Teissier which describes the local Euler obstruction as an alternating sum of the local polar multiplicities.